In a food processor, combine the basil and sugar.,Pulse until very finely ground.,The sugar should be bright green and look almost like pesto.,Combine the cream, milk, and basil-sugar in a large pot over medium heat.,Scrape out the seeds of the vanilla bean and add them to the cream mixture; put the pod in there too for extra flavor.,Simmer gently, stirring, until the sugar is dissolved, about 5 minutes.,______,In a large mixing bowl, whisk the egg yolks until slightly thick and yellow.,Gradually whisk half of the hot cream into the yolk mixture (do not add it too quickly or the eggs will scramble).,Return the entire mixture to the pot and whisk constantly over medium-low heat until the custard is thick enough to coat the back of a spoon and leaves a path when you run your finger across it, about 5 minutes; do not allow to boil.,Pass the custard through a fine-mesh sieve into a large container.,Chill the ice cream base completely in a large bowl full of ice water, stirring here and there.,Mix in the salt once completely cold.,Churn in an ice cream maker according to the manufacturers directions.,When done, the ice cream will be the consistency of soft serve.,To harden the ice cream fully, freeze in a covered plastic container.